Curriculum
Course: Mathematics — First Preparatory
Login

Curriculum

Mathematics — First Preparatory

Unit 1: Numbers

0/10

Unit 2: Algebra

0/4

Unit 3: Statistics

0/6

Unit 4: Geometry

0/6
Text lesson

Sets and Operations on Sets

Mathematics — First Preparatory

Sets and Operations on Sets

Worked examples

Worked examples

Comparison aspectMain ideaKeywords
•
  • Let A = {1
  • B = {4
  • 7} and U = {1
  • 10}
Example 1Find A ∪ B and A ∩ BFind
Solution
  • A ∪ B = {1
  • which has 7 elements. A ∩ B is the set of common elements
  • which is {4
elementscommon
Example 2Find A − B and B − AFind
Solution
  • A − B = {1
  • because these elements are in A but not in B. B − A = {6
  • 7}. Notice that A − B is not equal to B − A
becausetheseelementsNotice
Example 3Find the complement A′ with respect to the universal set UFindcomplementrespectuniversal
Solution
  • The elements in U but not in A are 6
  • 9 and 10. So A′ = {6
  • 10}. Check: n(A′) = 10 − 5 = 5
elementsCheck
Example 4
  • The opinions of 40 students were surveyed. 25 of them like football
  • 18 like basketball
  • and 9 like both. How many students like neither sport?
opinionsstudentsweresurveyed
Comparison aspectMain ideaKeywords
SolutionLet F be the set of students who like football and B the set of students who like basketball. The number who like at least one sport is n(F ∪ B) = 25 + 18 − 9 = 34. The number who like neither is 40 − 34 = 6 studentsstudentslikefootballbasketball
Example 5
  • If n(A) = 12
  • n(B) = 9 and n(A ∩ B) = 4
  • find n(A ∪ B)
  • then find n(A − B)
findthen
Solutionn(A ∪ B) = 12 + 9 − 4 = 17. The number of elements of A − B = n(A) − n(A ∩ B) = 12 − 4 = 8numberelements
Sets and Operations on Sets · 4 / 6